To understand the genetic basis of coping style in European seabass, fish from a full factorial mating (10 females x 50 males) were reared in common garden and individually tagged. Individuals coping style was characterized through behavior tests at four different ages, categorizing fish into proactive or reactive: a hypoxia avoidance test (at 255 days post hatching, dph) and 3 risk-taking tests (at 276, 286 and 304 dph). We observed significant heritability of the coping style, higher for the average of risk-taking scores (h2 = 0.45 ± 0.14) than for the hypoxia avoidance test (h2 = 0.19 ± 0.10). The genetic correlations between the three risk-taking scores were very high (rA = 0.96–0.99) showing that although their repeatability was moderately high (rP = 0.64–0.72), successive risk-taking tests evaluated the same genetic variation. A mild genetic correlation between the results of the hypoxia avoidance test and the average of risk-taking scores (0.45 ± 0.27) suggested that hypoxia avoidance and risk-taking tests do not address exactly the same behavioral and physiological responses. Genetic correlations between weight and risk taking traits showed negative values whatever the test used in our population i.e. reactive individual weights were larger. The results of this quantitative genetic analysis suggest a potential for the development of selection programs based on coping styles that could increase seabass welfare without altering growth performances. Overall, it also contributes to a better understanding of the origin and the significance of individual behavioral differences.